Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters

• Published in: PloS one Vol. 8; no. 12; p. e80821
• Main Authors: Matilainen, Kaarina, Mäntysaari, Esa A, Lidauer, Martin H, Strandén, Ismo, Thompson, Robin
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 10.12.2013; Public Library of Science (PLoS)
• Subjects: Algorithms; Analysis; Analysis of Variance; Animals; Biotechnology; Breeding; Breeding of animals; Cattle; Computational Biology - methods; Computational efficiency; Computer simulation; Computing time; Convergence; Dairying; Datasets; Economic models; Estimates; Food; Iterative methods; Likelihood Functions; Linear Models; Mathematical models; Maximum likelihood estimation; Methods; Monte Carlo Method; Monte Carlo simulation; Newton-Raphson method; Parameter estimation; Test procedures; Finland
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0080821

Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR), where the information matrix was generated via sampling; MC average information(AI), where the information was computed as an average of observed and expected information; and MC Broyden's method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden's method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.